作者: Afflict 時間: 2025-3-21 21:42 作者: 演繹 時間: 2025-3-22 01:52
https://doi.org/10.1007/3-540-30666-8Hamiltonian and reversible systems; Numerical integration; algorithms; calculus; differential equations 作者: STEER 時間: 2025-3-22 06:30
Common Problem Areas and Solutions,Hamiltonian systems form the most important class of ordinary differential equations in the context of ‘Geometric Numerical Integration’. An outstanding property of these systems is the symplecticity of the flow. As indicated in the following diagram作者: Repetitions 時間: 2025-3-22 12:03
Sian Adiseshiah,Jacqueline BoltonWe discuss theoretical properties and the structure-preserving numerical treatment of Hamiltonian systems on manifolds and of the closely related class of Poisson systems.We present numerical integrators for problems from classical and quantum mechanics.作者: 欺騙手段 時間: 2025-3-22 16:16
,Exposition: Identit?t(s)Brocken,One of the greatest virtues of backward analysis. is that when it is the appropriate form of analysis it tends to be very markedly superior to forward analysis. Invariably in such cases it has remarkable formal simplicity and gives deep insight into the stability (or lack of it) of the algorithm.作者: 欺騙手段 時間: 2025-3-22 19:00 作者: GIDDY 時間: 2025-3-22 22:08 作者: BURSA 時間: 2025-3-23 01:29
Non-Canonical Hamiltonian Systems,We discuss theoretical properties and the structure-preserving numerical treatment of Hamiltonian systems on manifolds and of the closely related class of Poisson systems.We present numerical integrators for problems from classical and quantum mechanics.作者: Exonerate 時間: 2025-3-23 06:44 作者: Nonporous 時間: 2025-3-23 13:23 作者: acrophobia 時間: 2025-3-23 15:16 作者: 連累 時間: 2025-3-23 21:28 作者: canvass 時間: 2025-3-24 01:24
Structure-Preserving Implementation,not deteriorate the correct qualitative behaviour of the solution.We study multiple time stepping strategies, the effect of round-off in long-time integrations, and the efficient solution of nonlinear systems arising in implicit integration schemes.作者: 采納 時間: 2025-3-24 06:16 作者: 畸形 時間: 2025-3-24 07:48 作者: OWL 時間: 2025-3-24 14:08
dBASE IV Lernen am Konkreten Beispielsses of numerical methods. We start with Runge–Kutta and collocation methods, and we introduce discontinuous collocation methods, which cover essentially all high-order implicit Runge–Kutta methods of interest. We then treat partitioned Runge–Kutta methods and Nystr?m methods, which can be applied t作者: 猛然一拉 時間: 2025-3-24 17:38
https://doi.org/10.1007/978-3-322-92882-5ed Runge–Kutta methods, and composition methods by using the notion of rooted trees and B-series. These ideas lead to algebraic structures which have recently found interesting applications in quantum field theory. The chapter terminates with the Baker- Campbell-Hausdorff formula, which allows anoth作者: 鼓掌 時間: 2025-3-24 19:31
Arbeitsbereich und Datenausgabe,n manifolds. Our investigation will follow two directions. We first investigate which of the methods introduced in Chap. II conserve invariants automatically. We shall see that most of them conserve linear invariants, a few of them quadratic invariants, and none of them conserves cubic or general no作者: locus-ceruleus 時間: 2025-3-25 00:50 作者: Optimum 時間: 2025-3-25 04:58
https://doi.org/10.1007/978-3-642-59076-4not deteriorate the correct qualitative behaviour of the solution.We study multiple time stepping strategies, the effect of round-off in long-time integrations, and the efficient solution of nonlinear systems arising in implicit integration schemes.作者: 生氣地 時間: 2025-3-25 09:20 作者: 圓木可阻礙 時間: 2025-3-25 15:19 作者: Traumatic-Grief 時間: 2025-3-25 19:48 作者: 表臉 時間: 2025-3-25 20:54 作者: 人類學(xué)家 時間: 2025-3-26 03:06 作者: 雄辯 時間: 2025-3-26 08:05 作者: 鋼筆記下懲罰 時間: 2025-3-26 08:54
Geometric Numerical Integration978-3-540-30666-5Series ISSN 0179-3632 Series E-ISSN 2198-3712 作者: 報復(fù) 時間: 2025-3-26 14:37
Examples and Numerical Experiments,ods. We deliberately consider only very simple numerical methods of orders 1 and 2 to emphasize the qualitative aspects of the experiments. The same effects (on a different scale) occur with more sophisticated higher-order integration schemes. The experiments presented here should serve as a motivat作者: 騙子 時間: 2025-3-26 17:55
Numerical Integrators,sses of numerical methods. We start with Runge–Kutta and collocation methods, and we introduce discontinuous collocation methods, which cover essentially all high-order implicit Runge–Kutta methods of interest. We then treat partitioned Runge–Kutta methods and Nystr?m methods, which can be applied t作者: Hormones 時間: 2025-3-27 00:59 作者: Coordinate 時間: 2025-3-27 02:37
Conservation of First Integrals and Methods on Manifolds,n manifolds. Our investigation will follow two directions. We first investigate which of the methods introduced in Chap. II conserve invariants automatically. We shall see that most of them conserve linear invariants, a few of them quadratic invariants, and none of them conserves cubic or general no作者: BLANK 時間: 2025-3-27 07:57
Symmetric Integration and Reversibility,s. We discuss reversible differential equations and reversible maps, and we explain how symmetric integrators are related to them. We study symmetric Runge–Kutta and composition methods, and we show how standard approaches for solving differential equations on manifolds can be symmetrized. A theoret作者: 明確 時間: 2025-3-27 12:34
Structure-Preserving Implementation,not deteriorate the correct qualitative behaviour of the solution.We study multiple time stepping strategies, the effect of round-off in long-time integrations, and the efficient solution of nonlinear systems arising in implicit integration schemes.作者: 外貌 時間: 2025-3-27 16:17
Hamiltonian Perturbation Theory and Symplectic Integrators, in what is for the theoretician a rather disappointing way. With modern calculating machines, one is now able to compute directly results even more accurately than those provided by perturbation theory.作者: Unsaturated-Fat 時間: 2025-3-27 21:02 作者: Debrief 時間: 2025-3-27 23:38
Dissipatively Perturbed Hamiltonian and Reversible Systems,ame is true for symmetric methods applied to non-reversible perturbations of reversible systems. In this chapter we study the behaviour of numerical integrators when they are applied to dissipative perturbations of integrable systems, where only one invariant torus persists under the perturbation an作者: HAWK 時間: 2025-3-28 05:29
Oscillatory Differential Equations with Constant High Frequencies,new complete function evaluation only after a time step over one or many periods of the fastest oscillations in the system. Various such methods have been proposed in the literature – some of them decades ago, some very recently, motivated by problems from molecular dynamics, astrophysics and nonlin作者: BROOK 時間: 2025-3-28 09:13 作者: 強(qiáng)化 時間: 2025-3-28 11:18 作者: progestogen 時間: 2025-3-28 15:54
Datenschutz und Datensicherheit,ffects (on a different scale) occur with more sophisticated higher-order integration schemes. The experiments presented here should serve as a motivation for the theoretical and practical investigations of later chapters. The reader is encouraged to repeat the experiments or to invent similar ones.作者: 預(yù)兆好 時間: 2025-3-28 20:46
dBASE IV Lernen am Konkreten Beispiellly all high-order implicit Runge–Kutta methods of interest. We then treat partitioned Runge–Kutta methods and Nystr?m methods, which can be applied to partitioned problems such as Hamiltonian systems. Finally we present composition and splitting methods.作者: 我不死扛 時間: 2025-3-28 23:18
https://doi.org/10.1007/978-3-322-92882-5recently found interesting applications in quantum field theory. The chapter terminates with the Baker- Campbell-Hausdorff formula, which allows another access to the order properties of composition and splitting methods.作者: 植物群 時間: 2025-3-29 04:45
Das relationale Datenbanksystem,Runge–Kutta and composition methods, and we show how standard approaches for solving differential equations on manifolds can be symmetrized. A theoretical explanation of the excellent longtime behaviour of symmetric methods applied to reversible differential equations will be given in Chap. XI.作者: 注視 時間: 2025-3-29 07:24 作者: 秘方藥 時間: 2025-3-29 13:22
,Pers?nlicher Anwendungsbereich,been proposed in the literature – some of them decades ago, some very recently, motivated by problems from molecular dynamics, astrophysics and nonlinear wave equations. For these methods it is not obvious what implications geometric properties like symplecticity or reversibility have on the long-time behaviour, e.g., on energy conservation.作者: 事物的方面 時間: 2025-3-29 16:33 作者: Infelicity 時間: 2025-3-29 23:02
Klaus von Sicherer,Eva ?underlíkovád becomes weakly attractive. The simplest example of such a system is Van der Pol’s equation with small parameter, which has a single limit cycle in contrast to the infinitely many periodic orbits of the unperturbed harmonic oscillator.作者: 放縱 時間: 2025-3-30 03:25 作者: 煉油廠 時間: 2025-3-30 04:23 作者: Accord 時間: 2025-3-30 12:04
Oscillatory Differential Equations with Varying High Frequencies,inate transforms that separate slow and fast motions and relate the fast oscillations to the skew-hermitian linear case. For the numerical treatment we consider suitably constructed long-time-step methods (“adiabatic integrators”) and multiple time-stepping methods.作者: mechanical 時間: 2025-3-30 12:53
Examples and Numerical Experiments,ffects (on a different scale) occur with more sophisticated higher-order integration schemes. The experiments presented here should serve as a motivation for the theoretical and practical investigations of later chapters. The reader is encouraged to repeat the experiments or to invent similar ones.作者: defenses 時間: 2025-3-30 16:32
Numerical Integrators,lly all high-order implicit Runge–Kutta methods of interest. We then treat partitioned Runge–Kutta methods and Nystr?m methods, which can be applied to partitioned problems such as Hamiltonian systems. Finally we present composition and splitting methods.作者: 勤勞 時間: 2025-3-30 23:35
Order Conditions, Trees and B-Series,recently found interesting applications in quantum field theory. The chapter terminates with the Baker- Campbell-Hausdorff formula, which allows another access to the order properties of composition and splitting methods.作者: 破布 時間: 2025-3-31 01:19 作者: 執(zhí) 時間: 2025-3-31 07:01 作者: Infiltrate 時間: 2025-3-31 12:27
Oscillatory Differential Equations with Constant High Frequencies,been proposed in the literature – some of them decades ago, some very recently, motivated by problems from molecular dynamics, astrophysics and nonlinear wave equations. For these methods it is not obvious what implications geometric properties like symplecticity or reversibility have on the long-time behaviour, e.g., on energy conservation.作者: osteopath 時間: 2025-3-31 16:53
Arbeitsbereich und Datenausgabe,hem. In particular, we study projection methods and methods based on local coordinates of the manifold defined by the invariants. We discuss in some detail the case where the manifold is a Lie group. Finally, we consider differential equations on manifolds with orthogonality constraints, which often arise in numerical linear algebra.
